A strategy is presented for teaching arithmetic to students with mental retardation, based on subitizing, skill of recognizing number of objects in a set without actually counting, and pattern recognition. The strategy helps children understand concept of addition by representing number configurations on 5-frames and 10-frames, and reduces need…

Provides an overview of the conceptual analysis of the unit fraction that provided the framework for developing a comprehensive array of fraction activities for fourth-grade students. Reveals the students' difficulties in learning the unit-fraction concept and discusses the didactical implications of these difficulties. Contains 15 references.…

Examines students' understanding of the quantitative relationships, operations, and properties of relationships and operations that are introduced in arithmetic and beginning algebra courses. Develops alternative approaches to the teaching of structure such as the structural-to-computational model and the procedural-to-structural model. Concludes…

For the last several years teachers have been using counters and connected cube "trains" and creating base-10 block models to help students develop number sense and understand number concepts. It is described how ten-frame tiles could be more useful tool for building number understanding for many students.

A teacher shares his successful experience in helping students understand the relationship between exponents and logarithms in high school and college courses. He presents the procedure that he used for teaching using a graphing calculator that shows previous calculations made.

This two-volume teacher's guide is to be used with a first-semester, third-grade mathematics program. The program is in large part the outgrowth of involvement with children and was influenced by information gathered in an extended pilot project conducted nationwide during 1975-79. The manner of presentation and the pedagogical ideas and tools are…

This two-volume teacher's guide is to be used with a second-semester, third-grade mathematics program. The program is in large part the outgrowth of involvement with children and was influenced by information gathered in an extended pilot project conducted nationwide during 1975-79. The manner of presentation and the pedagogical ideas and tools…

This article explores the origins and potential benefits of the empty number line for the development of mental computation. It also provides a learner's perspective of its use through the reflections of nine-year-old Emily. (Contains 3 figures.)

This article describes how the story of Alice in Wonderland helps students understand the operation of multiplying by a rational number less than 1 and related aspects of ratio and proportion. Included with this article is a "How Tall Is Alice?" Worksheet. (Contains 1 table and 6 figures.)

Children's literature can play a significant role in integrating math and science concepts into real-world applications. One particularly delightful selection is "Cucumber Soup" (Krudwig, 1998). This book can create a context--making cucumber soup--for weighing and for a real-life on adding fractions. This kind of learning context takes children…

The aim of this series of four articles is to look critically, and in some detail, at the primary strategy approach to written calculation, as set out on pages 5 to 16 of the "Guidance paper" "Calculation." The underlying principle of that approach is that children should use mental methods whenever they are appropriate, whereas for calculations…

This article describes a recent and successful initiative on teaching place value and the decomposition method of subtraction to pupils having difficulty with this technique in the 9-12-year age range. The aim of the research was to explore whether using the metaphor of selling chews (i.e., sweets) in a tuck shop and developing this into an iconic…

Fourth grade children (n=20) were matched on a pretest and randomly assigned to either a wooden base-10 block or computerized microworld group. Instruction was designed to establish relationships between notation and meaning, extending whole number numeration to decimal numeration. Neither group changed whole-number notational methods nor had…

The paper describes evolution of an approach to teaching mathematically disabled and slow learning students through a Piagetian framework. It is explained that a step-by-step procedure is used to internalize material actions into mental actions via perception and verbalization. Formulae are introduced early, and emphasis is placed on promoting…